Wow.
Fallen, let me make sure I understand this. You became involved with a woman who's about to go through a divorce and become single mother -- a woman who will shortly have no backup at home when it comes to keeping her kids' emotional worlds stable through divorce, and who will be responsible for doing the lion's share of the breadwinning in her household -- and who has a long, long commute. You made promises to her, then pulled the rug out from under her, totally shredded and humiliated her. And she's looking for another job? If it's because of the commute or because she's had an offer of more money elsewhere, that's one thing, but if it's because of you -- why aren't you the one looking to move on from there? She has a network of friends and colleagues, a reputation, presumably some seniority; why should she lose it all because you weren't clear about what you wanted?
If you're going to pull out of her world after all that, I really think you should do it all the way, rather than making things harder on her and her kids, emotionally and maybe financially, by sitting there in her professional world. It sounds like you're a radiologist; are there no other hospitals or outpatient clinics in the area?
Finally, please don't try to smooth things over with her. Don't try to talk to her if she doesn't initiate it. She has a perfect right to loathe, despise, hate, etc. you. Let her get on with it and deal with it. You want things to be smooth because you can't bear the thought of her thinking about you this way, but this is really selfish; it's about you. Just step back from that and let her get on with the most important job she has, which is to take care of herself and her children through one of the hardest times in their lives, which you've just made harder. is it awful and painful for you, sure, yes, but I guarantee she's got a harder road. And -- finally -- please don't send her an email telling her what a hero you're being by stepping back and letting her do this without interference, wishing her the best, etc. Because that's also, really, for your own benefit.
I find this is a very common thing, by the way -- married men getting involved with single mothers, and having no idea how much energy they have to devote to childrearing, how much their children depend on them, and how important it is that the mothers be emotionally healthy and happy so that they can care for those children. Because the men by and large have wives who do most of the childrearing in their own homes, and of course the children don't really exist in the context of the affair. Please, fellas, respect the jobs those women are doing, as well as the needs of the children.